You can analyze the Cu concentration by ICP and calculate CuO concentration. You can also use X-Ray Florescent (XRF) for analyzing the CuO in your solution.
You can go for X-ray photoelectron spectroscopy to examine the elemental composition . To characterize the optical properties of CuO, you can go for UV-vis absorption spectroscopy and to study the crystal structure, there is X-ray diffraction and Raman Spectroscopy.